Question

A car is accelerating uniformly as it passes two checkpoints that are 30 m apart. The time taken between checkpoints is 4.0 s and the car’s speed at the first checkpoint is 5.0 m/s. Find the car’s acceleration and its speed at the second checkpoint. (calculus based)

Answer 1

Using the kinematic formula (see https://www.khanacademy.org/science/physics/one-dimensional-motion/kinematic-formulas/a/what-are-the-kinematic-formulas), obtain the following.

The speed at the second checkpoint $v$ can be found from the formula:

$$d = \dfrac{v+v_0}{2}t$$

where $d = 30m, v_0 = 5m/s,t = 4s$. thus, obtain:

$$v = \dfrac{2d-v_0t}{t} = \dfrac{2\cdot 30m- 5m/s\cdot 4s}{4s} = 10m/s$$

The acceleration is then (by definition):

$$a = \dfrac{10m/s-5m/s}{4s} =1.25m/s^2 \approx 1.3m/s^2$$

Answer. speed: 10m/s, acceleration: 1.3m/s^2.S